求定积分:∫(上标是2 ,下标是0)(e^x)/[(e^x-1)^(1/3)]dx=

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求定积分:∫(上标是2 ,下标是0)(e^x)/[(e^x-1)^(1/3)]dx=
求定积分:∫(上标是2 ,下标是0)(e^x)/[(e^x-1)^(1/3)]dx=

求定积分:∫(上标是2 ,下标是0)(e^x)/[(e^x-1)^(1/3)]dx=
设:(e^x-1)^(1/3)=y e^x-1=y^3 e^x=1+y^3 e^xdx=3y^2dy
∫(2,0)e^xdx/(e^x-1)^(1/3)
=3∫[(e^2-1)^(1/3),0] y^2dy/y
=3∫[(e^2-1)^(1/3),0] ydy
=1.5 y^2 | [(e^2-1)^(1/3),0]
= 3[(e^2-1)^(2/3)]/2

原式=∫(0→2)d(e^x)/(e^x-1)^(1/3)=3/2(e^x-1)^(2/3)|(0→2)=3/2(e^2-1)^(2/3)